University Logic Course: Homework on Venn Diagrams and Truth Tables

This document presents solutions to a logic homework assignment. The assignment addresses several key concepts in logic, including the advantages and disadvantages of using Venn diagrams and rules to test for validity, and the different types of logic (inductive and deductive). It explains the meaning of conditional statements and the method for using a complete truth table to test an argument's validity. Additionally, the assignment explores the differences between Group I and Group II rules in logical deductions. The solutions are supported by references to academic sources, providing a comprehensive understanding of the topics covered. This resource is valuable for students studying logic and seeking to understand and solve similar problems.

1. What are the benefits and detractions of choosing Venn diagrams and rules as tests
for validity?
Answer.
The primary benefit of choosing Venn diagrams and rules as a test for validity lies in
its graphical presentation. The diagrams are the designs that are typically useful for
communicating information and are able to be presented in different forms (Shin, 1996). Due
to this reason people are able to understand the information easier or the visualization of
concepts are easier. However the kind of diagrams and rules raises complication when
dealing with many objects. Venn diagrams are considered for three most circles and has eight
regions which means the diagrams become difficult to interpret if there are more than the
limited of number of figures or diagrams.
2. Why are there two kinds of logic? Does each have its own advantage, or is one clearly
better than the other?
Answer.
There are mainly two types of logic- inductive and deductive as it broadly classifies
the formation of thoughts, opinions and judgements of logic or principle of correct reasoning.
The fundamental of a logical argument lies in its statement or proposition where the
propositions are used for building arguments (Shin, 1994). Among the two, deductive kind of
logic is better than inductive since complete evidence of the truth is provided in deductive
type of reasoning and leads to a specific and accurate conclusion unlike inductive.in case of
inductive, it considers only specific information and provides a broad generalization where
the results are probable and are usually established based on repeated experiences.
3. What exactly does the conditional mean, if not the usual "if-then"?
Answer.
The actual assertion of conditional means if an antecedent is true then the
consequence is also universal and true. Also any conditional consisting of a true antecedent
and false consequent is false. A Conditional statement is usually a compound statement “if a,
then b”, where ‘a’ is the antecedent and the ‘b’ is consequent (Strawson, 2017).

The usual “if-then” statements in English cannot be termed as the conditional as the
operator becomes false if the conditional statements are translated into “if-then” (Scruton,
2004). For instance if P and Q are conditional statements and translated into English “If P is
true then Q is true”. However this does not validate statement and produce false result for
conditional. In logic conditional operator always a true formula is produced if consequent is
true even if antecedent is false.
4. Explain the method for using a complete truth table to test an argument for validity.
Answer.
Three steps process are generally adopted for testing an argument of its validity by
using a complete truth table. First each premises and the conclusion are symbolized for the
argument. Second, the truth table is made where column is drawn for each premise and for
each conclusion. Third step is for testing if the truth table shows the row where every premise
column is true and the conclusion column is false, then the argument is considered as invalid
(Rescher and Anderson, 1962). Otherwise the argument is considered as valid.
5. What are the differences between the ways of using Group I rules and Group II rules
in logical deductions?
Answer.
During logical deductions, there are few different approaches between using Group I
rules and Group II rules. The Group I rules uses reasoning by certainty which is approached
through top down reasoning. This reasoning method deals with certainty and the method
follows certain facts and rules. The Group II rules uses bottom up reasoning which means
reasoning by consistency (Strawson, 2012). Here the reasons are drawn from specific facts
and looks patterns in data and generally start deducting logics through specific observation
from available data.

References
Bergkvist, L. and Rossiter, J.R., 2007. The predictive validity of multiple-item versus single-
item measures of the same constructs. Journal of marketing research, 44(2), pp.175-184.
Rescher, N. and Anderson, A.R., 1962. Conditional permission in deontic
logic. Philosophical Studies, 13(1-2), pp.1-8.
Scruton, R., 2004. A short history of modern philosophy: From Descartes to Wittgenstein.
Routledge.
Shin, S.J., 1994. The logical status of diagrams. Cambridge University Press.
Shin, S.J., 1996. Reasoning with Venn Diagrams. Logical reasoning with diagrams, 6, p.81.
Strawson, P. F. 2017. Subject and predicate in logic and grammar. Routledge.
Strawson, P.F., 2012. Introduction to Logical Theory (Routledge Revivals). Routledge.